"Zero Exponent Powers and Negative Integer Exponent Powers" PPT courseware

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"Zero Exponent Powers and Negative Integer Exponent Powers" PPT courseware

1. Review questions

1. Recall the properties of operations for powers of positive integer exponents:

(1) Multiplication of powers with the same base: am·an=am+n (m and n are positive integers)

(2) Power of power: (am)n=amn (m, n are positive integers)

(3) Power of product: (ab)n=anbn (n is a positive integer)

(4) Division of powers with the same base: am÷an=am-n (where a≠0, m,n are all positive integers, and m>n)

(5) Power of quotient: (a/b)n=an/bn (n is a positive integer);

2. am÷an=am-n (where a≠0, m,n are all positive integers, and m>n)

When dividing formulas for powers with the same base,

There is an additional condition: m>n, that is, the exponent of the dividend is greater than the exponent of the divisor. What happens when the exponent of the dividend is not greater than the exponent of the divisor, that is, m = n or m < n?

Exploration 1: The meaning of zero exponent powers

If m=n,

The rule of division of powers with the same base is discovered based on the meaning of division

Regulation: a0=1(a≠0)

Any number not equal to zero raised to the zero power is equal to 1.

Zero raised to the zero power is meaningless.

Exploration 2: The meaning of negative integer exponent powers.

If m

Rule of division of powers with the same base: Meaning of division: Discovery:

Regulation: a-n=1/an (a≠0, n is a positive integer)

Any number not equal to zero raised to the -n (n is a positive integer) power is equal to the reciprocal of this number raised to the n power.

Summary: Tell us what you learned from this lesson?

1. The meaning of zero exponent power

a0=1(a≠0)

2. The meaning of negative integer exponent power.

a-n=1/an(a≠0,n is a positive integer)

3. Zero exponent power and negative integer power are introduced. The range of exponents is expanded to all integers, and the properties of power still hold.

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Update Time: 2024-09-02

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